# How to find the homogeneous equation of non-homogeneous equation?

I have homework and I don't understand the request.

this is the task: (I'm translating from Hebrew, so I'm sorry for unclear details, if there are):

Solve the following linear equations , and write down the solution of the appropriate homogeneous equation.

What does he mean, "to write down the solution of the appropriate homogeneous equation"?

What is the appropriate homogeneous equation?

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In this case your system is of the form $A\bar{x}=\bar{b}$, where the matrix $A$ is \begin{bmatrix} 1 & 1 & 1\\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{bmatrix} and $\bar{x}=(x_{1},x_{2},x_{3})$, $\bar{b}=(1,1,1)$. The appropriate homogeneous equation is simply $A\bar{x}=\bar{0}$, where $\bar{0}=(0,0,0)$. So in practise, you just replace the constants on the right hand sides of your linear system to equal zeros in order to obtain the homogeneous equation.
I think he wanted to solve the system which has $0$ instead of $1$ on LHS. Therefore, it is clear that $x_1=x_2=x_3=0$ is its trivial solution